The Variations in Elastic and Inelastic Seismic Demand - Research Proposal Example

Evaluation of The Variations in Elastic and Inelastic Seismic Demand and Capa of MRSF with Vertical Geometric Irregularities A Proposal Submitted in partial fulfillment of the requirement for the Degree of Doctor of Philosophy Submitted by Duygu Kayikci (2003-07) Approved: ---------------------- ---------------------- Dr. Michael Phang Dr. Singiresu S Rao Committee Chairman Committee Member ---------------------- ---------------------- Dr. Wimal Suaris Dr. Ronald F. Zollo Committee Member Committee Member ---------------------- ---------------------- Dr. Gulay Altay Dr. Ronald F. Zollo Outside Member Committee Member University of Miami Miami Contents Page Summary 3 1. Introduction .... 4 1.1 Background and motivation of the study .... 4 1.2 Historical performance of MRSF with vertical geometric irregularity 5 1.3 Codified description and approach for vertical geometrical irregularity 5 1.4 Review of related literature ...... 6 2. Problem Statement .. 7 3. Objective of the Study .. 9 4. Methodology . 9 4.1 Description of vertical geometrical irregularity/architectural setback 9 4.2 Ground motion record . 9 4.3 Methods of analysis and evaluation approach . 10 5. Conclusions . 11 Figures . 12 Table . 14 References . 15 SUMMARY Earthquake resistant design codes and provisions set significant limitations on the structural irregularity. The present study examines and analyses the procedures used in determining seismic demands. The study also suggests scope for future investigations to determine if these limitations are sufficient to ensure intended performance objectives for structures with vertical irregularities. As part of previous studies conducted on code specified types of irregularities in different building systems of various material and height, this study comprehensively evaluates the variations in elastic/inelastic, static and dynamic seismic demands. In addition the study also looks into the capacity of low rise Moment Resisting Steel Frames (MRSF), with vertical geometric irregularities in forms of uniform setbacks and investigates the adequacy and limitations of different analysis procedures in predicting these parameters. The main parameters used for investigating the effects of geometric irregularities were; (a) Horizontal dimensions, and (b) Extended uniform setbacks. The analysis is conducted using total 24 two-dimensional five-story, five-bay MRSF models that cover all possible combinations of the vertical and horizontal dimensions of uniform setbacks. The effects of irregularities and variations in elastic demands, in response to earthquakes, will be investigated and compared through; (a) Modal properties (b) Elastic base shear strength demands (c) Elastic story shear strength demand (d) Global displacement demands (e) Story drift demands (f) Elastic multi degree of freedom systems (MDOF) modification factor. Variation in these parameters is determined using accepted linear static and dynamic procedures. During the study, the variation in inelastic capacities will also be evaluated and compared through; (a) Base and story yield shear strengths (b) Global and story ductility capacities (c) Failure mechanisms and ultimate strengths (d) Inelastic seismic design coefficients such as; structural ductility factor (), ductility reduction factor (R), structural over-strength factor () and their distributions using nonlinear static procedure, namely push-over analysis. The limitations and adequacy of each analysis procedure in predicting demand and capacities of buildings with specific amount of irregularity will also be evaluated by comparison with the results obtained from "exact" nonlinear time-history analysis procedure. The study is expected to define, 'limit states' of uniform setbacks, for the application of each procedure determining seismic demands and capacities. 1. INTRODUCTION 1.1 Background and Motivation of the study Design of a building with vertical geometric irregularity to resist earthquake loads is a challenging problem that structural engineering needs to overcome early in the conceptual design phase. Geometric irregularities in the forms of architectural setbacks that are either outcome of planning and zoning regulations or aesthetical concerns of owners and architects, are considered as a type of vertical irregularity if it exceeds the limits set by earthquake resistant design codes and provisions. The main scope of this study was developed parallel to the approaches and evaluation perspectives of the earthquake resistant design codes and guidelines on vertical irregularities. In a broader sense, the intention was to obtain results for the implication of seismic design codes and provisions related to vertical geometric irregularities on low-rise Moment Resisting Steel Frames (MRSF). Earthquake resistant design provisions and guidelines approach vertical geometric irregularity as a factor that reduces reliability of seismic demands and capacities defined by simplified procedures. Codes are encouraged to provide as much redundancy and regularity as possible in the seismic-force-resisting system of buildings. In this context, many of the adverse effects due to vertical geometric irregularities are expected to be minimized by appropriate selection of analysis procedure that is used in determining seismic demands and its distribution. This necessitates in-depth understanding of; (a) Variations of elastic and inelastic, static and dynamic, seismic demand/capacity ratios and their distributions along the height of frames. (b) Variations in adequacy of each analysis procedure in predicting related parameters with changes in degree and extents of setbacks. As a result, there is need for a knowledge base early in the conceptual design phase that provides quantitative information on the critical amount of vertical geometric irregularity for each analysis procedure, or least rigorous analysis procedure that must be employed for determining seismic demands and capacity of low-rise MRSF with specific amount of vertical irregularity. This will help in predicting the seismic performance within a given confidence interval. 1.2 Historical performance of MRSF with vertical geometric irregularity In order to understand the effects of vertical geometric irregularity on seismic performance of MRSF, post inspection studies conducted after the 1994 Northridge earthquake were reviewed in detail. A precise and accurate conclusion can not be determined about the correlation between vertical geometric irregularity and seismic performance due to lack of data about structural details, time histories of actual ground motion records, severity of such occurrences and the points when the damage was observed. After reviewing the survey reports, it was observed that there is a need for detailed numerical study to assess the correlation between the change in severity of damage and the size of setbacks for low-rise MRSF. 1.3 Codified description and approach for vertical geometrical irregularity Earthquake resistant design provisions and guidelines classify irregularity in two main categories, namely plan irregularity and vertical structural irregularity. Vertical irregularities include; (1) Stiffness irregularity-soft story (2) Weight /mass irregularity (3) Vertical geometrical irregularity (4) In-plane discontinuity in vertical lateral-force-resisting elements (5) Discontinuity in capacity-weak story. Vertical irregularity is considered as a factor that reduces adequacy of simplified analysis procedure in calculating seismic demands and its distribution. Therefore, earthquake resistant design provisions and guidelines require a preliminary evaluation procedure to assess the presence of irregularity and to select minimum level analysis that must be employed in determining seismic demands. Lateral force resisting systems with uniform distribution of mass, stiffness and strength and below the prescribed amount of deviation in horizontal dimension of a story were considered as regular. In general, dynamic procedures are recommended for irregular building in which the contribution of higher mode effects to dynamic behavior is significant. Nonlinear procedure is required if structures are subjected to large magnitude earthquakes which induce inelastic seismic demands. In order to determine whether the description of a vertical geometric irregularity and limitations set for analysis procedure is sufficient to ensure achievement of the intended performance level for low rise MRSF, related requirements of the latest seismic design code and provisions were reviewed and compared in detail. Vertical geometric irregularity in the form of setback, is assessed by the ratio of horizontal length of setback to base floor. If the ratio of horizontal dimension is above the limit prescribed by the code, the building is considered "irregular". According to 1997 Uniform Building Code, Section 1629.8.4 (UBC & ICBO 1997) and Table 16-L, buildings with setback are considered as a case of vertical geometric irregularity; if the horizontal dimension of the lateral force resisting systems in any story is more than 130 % of that in an adjacent story, see Figure 1-1. Equivalent Lateral Force (ELF) procedure allowed determination of seismic demands on buildings with vertical geometric irregularity if the structures are not more than five stories or 65 feet in height. The parameters used to describe vertical geometric irregularity and limit set for selection of appropriate analysis procedure by 1997 National Earthquake Hazards Reduction Program - NEHRP (FEMA 302, FEMA 303) and its later Versions; 2000 NEHRP (FEMA 368), 2003 NEHRP (FEMA 450), were similar and equivalent to 1997 UBC and 2000 IBC. NEHRP commentary illustrated two additional cases of vertical geometric irregularity. According to NEHRP Commentary, buildings with uniform setback are considered irregular if the horizontal length of a cut-off is 15% larger than base floor, see Figure 1-2. Eurocode 8, in addition to horizontal dimension, used "relative height of first uniform setback" as a determinant of critical amount of irregularity. Lateral force resisting system with uniform setback is considered irregular if (a) The total horizontal length of cut-off, A1 and A2 is initiated above 15 % of the total height of frame, H is 20 % higher than the previous plan dimension L, as shown in Figure 1.3(a). (b) Total horizontal length of cut-off, A1and A2, initiated below 15 % of the total height of frame, H, is 50 % higher than the previous plan dimension, L, as shown in Figure 1-3(b). 1.4 Review of related literature Generally, studies conducted to define the vertical irregularity differed in terms of (a) the type of irregularity studied (b) the lateral force resisting system used in evaluations (c) the construction material used in the building and (d) height of the building. Humar & Wright (1977) studied dynamic behavior- frequencies and mode shapes of a series of multistory steel rigid-frame buildings with setback irregularities. Aranda G.R (1984) focused on ductility demands for reinforced concrete (R/C) frames irregular in elevation. Moehle & Alarcon (1986) performed combined experimental and analytical studies on a nine story reinforced concrete building with and without vertical stiffness discontinuity. Shahrooz & Moehle (1990) evaluated the seismic response of a building designed with setback irregularity using experimental and analytical study. They tested one-quarter scale model of a six-story, two-bay by two-bay ductile moment-resisting reinforced concrete building having a 50% setback at mid-height. Wong & Tso (1994) studied seismic loadings for buildings with setbacks. They focused on two main factors, (a) determination of the period of vibrations (b) lateral force distribution without considering contributions of higher modes. Valmundsson & Nau (1997) studied seismic response of 5, 10 and 20 story steel framed structures with vertical irregularity using a 2D generic model. In addition to mass, stiffness and strength type of vertical irregularities, Ali (1998) studied the effect of setback irregularity using four different 10-story, 2-D generic steel frame models with combinations of different mass and stiffness ratios. Chintanapakdee & Chopra (2004) investigated effects of strength, stiffness and mass irregularities on seismic demands of 12-story steel frames using time history analysis. Tremblay & Poncet (2005) investigated seismic performances of concentrically braced steel frames with mass irregularities through seven different, 8-story concentrically braced steel frames with setbacks. After reviewing previous studies, it was observed that there are a limited number of studies conducted on the effect of vertical geometric irregularity on low-rise steel buildings with moment resisting steel frames (MRSF). Besides, studies conducted on MRSF were limited with only a few cases with specific rates of reduction in combination of mass, stiffness and strength reductions, using single bay generic frames, rather than variation in geometric dimensions of setbacks as described by seismic design codes. In addition, as noted by Al-Ali & Krawinkler (1998) there is a significant disagreement on the effects of setback irregularity on seismic behavior and adequacy of simple linear static procedure in predicting seismic demands on these types of buildings. Therefore, there is a strong need to asses the effects of vertical geometric irregularity on low rise MRSF, including the change in redundancy inherent in the nature of setback with the parameters consistent with seismic design codes. The study must be comprehensive enough to include each possible change in extends and horizontal dimension of setback in five story five bay MRSF. 2. Problem statement The main problem related with setback irregularities lies in differences in elastic and inelastic dynamic strength and displacement demands and capacities compared to that of regular configurations along with uncertainties of the analysis procedure in predicting these parameters. Assuming that all other uncertainties are avoided, the capabilities of buildings to satisfy design performance objectives within given certainty depends on the amount of irregularity and the analysis procedure used to design level shear strength and displacement demands. Buildings with vertical geometric irregularity above certain amounts may not satisfy performance objectives if they are designed according to seismic demands, or calculated by methods that do not consider dynamic and inelastic behavior accurately. Equivalent linear static force procedure can be inadequate in predicting elastic and inelastic shear strength/ displacement demands and their distribution. On the other hand more rigorous, linear dynamic procedures may give errors in predicting inelastic seismic strength and displacement demands and capacities. Limitation of design level of seismic demands, that were calculated from linear static and dynamic procedures, originate from the approximation requiring shear strength of multi degree of freedom (MDOF) systems. It can be calculated by modifying elastic first mode spectral acceleration with response modification factor R at a given ductility . These factors are derived from elastic and inelastic responses of first mode single-degree-of-freedom (SDOF) systems and may only be adequate to represent inelastic seismic behavior of MDOF up to certain amount of vertical irregularities. These inelastic design parameters have been established by considering the characteristics of a typically regular and properly designed structure. Therefore there is a significant need to define the variation in seismic demands and capacities, and asses the critical level of irregularity above which additional uncertainties can not be tolerated at a given analysis procedure. 3. Objective of the Study The main intention of the study is to develop a better understanding of elastic and inelastic behaviors of MRSF with a range of geometric irregularity, so that better judgment can be made during architectural and engineering conceptual design processes. Therefore, the present study is aimed to define the critical level of irregularity that causes significant difference in elastic versus inelastic, static versus dynamic seismic demand/capacity as well as accuracy of each analysis methods in predicting the behavior. 4. Methodology 4.1 Description of vertical geometrical irregularity/architectural setback Variations in seismic behavior with change in size of setbacks were evaluated with respect to hypothetical five story-five bay regular model. Variations in vertical geometric irregularity or architectural setback were described by (a) Degree of irregularity, DGI (b) Extent of setback, Hs. To keep parameters consistent with the ones defined by earthquake resistant design guidelines and provisions, both parameters are measured by the ratio of geometric dimensions. DGI is measured by the ratio of horizontal length of the setback to the horizontal length of base floor. Hs is measured the ratio of number of storeys along which setback extends (step size of setback) to the total number of story. The degree of setback is to be increased by reducing the number of bays at floor frames while the extent of setback are to be increased by moving down the initiation level of the first storey of tower part. To ensure meaningful comparison of elastic, inelastic, static and dynamic response of buildings, the fundamental vibration period at first mode and damping properties are kept the same for all geometrically irregular models shown in figure 1.4. 4.2. Ground motion records Two different sets of time history records will be employed to evaluate variations in elastic and inelastic demands and capacity and adequacy of each analysis procedure in predicting these parameters. The first set of records will be selected from seismic hazards with 10 % probability of exceedance in 50 years with spectral acceleration value compatible with design spectrum at characteristic periods of soil profile and at first mode periods of structure. A second set of ground motions will be selected among actual records that represent 2 % probability of exceedance in 50 years to evaluate seismic demand under the most severe conditions. The characteristics of the ground motion records employed in the study were shown in Table 1.1. 4.3. Methods of analysis and evaluation approach The objectives will be accomplished by calculating and comparing the variations in engineering demands and capacities through all analysis methods specified by NEHRP (2003) using SAP 2000 V.8 computer program. The procedures used in this study, by the order of increasing rigor and expected accuracy, are given below; Equivalent Linear (elastic) Static Analysis of MDOF (ELF) Linear Dynamic Analysis of MDOF: a) Modal analysis b) Response spectrum analysis using SRSS modal combination of 1997 NEHRP smoothed response spectrum c) Response spectrum analysis using SRSS modal combination of scaled ground motion records Linear Direct Time History Analysis, LTH Nonlinear Static Analysis -"Push over" Analysis, NSP Nonlinear Direct Time History Dynamic analysis, NTH The variations in dynamic behavior with horizontal and vertical dimensions of setback must be evaluated through changes in modal properties. Using modal properties of each irregular model, it was also expected to derive correlation between modal properties and seismic demands and capacities, and express critical levels of setback dimension in terms of more general modal properties. Variations in lateral forces in response to ground motion needs to be evaluated through variations in; (a) In base shear strength demands (b) In story shear strength demands (c) In global displacement and elastic MDOF modification factor (d) In distribution of story drift, using all linear analysis methods specified in seismic design code. Seismic demands defined from all procedures need to be compared with the ones defined from nonlinear direct time history analysis. Nonlinear analysis of dynamic response, by direct integration of the coupled equations of motion, is considered as "exact" method of analysis. Therefore, the ratio of the seismic demand parameters defined from NTH to other analysis procedures enable us to define uncertainties of each analysis procedure and confidence interval of satisfaction of specific performance objective. Variations in the following need to be determined using nonlinear static analysis -"Push over", using three elastic distributions by NEHRP 2003. (a) Base shear strength and displacement capacity (b) Story shear strength and drift distribution (c) Failure mechanism with change in degree The variation in seismic capacity obtained from all three lateral force distribution methods need to be compared so that the adequacy of each distribution in determination of shear strength and displacement of irregular mode is assessed. 5. CONCLUSIONS In conclusion, the aim of the study is to contribute to the knowledge base in the subject area of seismic response of irregular buildings, for the assessment of the critical level of irregularity that shows significant changes in elastic and inelastic seismic capacity/demand ratios when compared to regular structures. In addition the study is aimed at defining critical level of setbacks after which a specific analysis procedure is not able to predict exact behavior or determine the most reliable analytical procedure that can be employed for buildings with a specific degree of irregularity. Figure 1.1 1997 NEHRP - Schematic Descriptions of Vertical Geometric Irregularities . Figure 1.2 1997 NEHRP - Schematic descriptions of Vertical Geometric Irregularities Figure 1.3 Definition of Geometric Irregularity According to Euro Code 8 Figure 2.1 Inelastic Force Deformation Curve. [ Figure C4.2-1 of NEHRP 2003 Commentary] 0.2 0.4-SYM 0.4-NSYM 0.6-CSYM 0.6-NSYM 0.8-SYM 0.8-NSYM M11 M 12 M13 M14 M15 M16 M17 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 M21 M22 M23 M24 M25 M26 M27 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 M31 M32 M33 M34 M35 M36 M37 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 M41 M42 M43 M44 M45 M46 M47 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 Figure 1.4 Model with Different Degree and Extend of Vertical Geometric Irregularity. Station Earthquake, year Magnitude Closest distance to fault (km) Soil Type Peak Ground Acceleration (cm/sec^2) Peak Ground Velocity (cm/sec) Peak Ground Displacement (cm) Group I Los Angeles Baldwin Hill, 900 Northridge CA, 1994 6.7 31.3 USGS ( B ) NEHRP(C) 234.2 14.9 6.17 Century City Lacc North, 900 Northridge CA, 1994 6.7 25.7 USGS (B ) NEHRP(C) 250.7 21.4 6.68 Santa Monica City Hall, 3600 Northridge, CA1994 6.7 27.6 USGS(B) NEHRP(C) 362.6 25.1 7.16 Saratoga Aloha Avenue, 00 Loma Prieta CA ,1989 7.1 13 USGS(B) NEHRP(C) 494.5 41.3 16.2 Castaic-Old Ridge Route, 900 Northridge CA, 1994 6.7 22.6 USGS ( B ) NEHRP(C) 557.1 52.1 4.21 Group II Newhall L.A county Fire station, 900 Northridge CA, 1994 6.7 7.1 USGS ( C ) 571.6 75.5 17.6 Taichung, Taiwan, 00 Chi-Chi, Taiwan 1999 7.6 43.44 USGS(B) NEHRP(C) 679.9 48.5 24.45 Sylmar County Hospital ,3600 Northridge CA, 1994 6.7 6.4 USGS ( C ) 826.8 128.9 32.68 Santa Monica City Hall , 900 Northridge, CA1994 6.7 27.6 USGS(B) NEHRP(C) 866 41.7 15.09 Table 1.1 Characteristic of Ground Motion Recorded Used in the Study References: Al-Ali, A.A.K., and Krawinkler, H., "Effect of Vertical Irregularities on Seismic Behavior of Building structures," Stanford University, California, 1998. 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FEMA-274., "NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings," Federal Emergency Management Agency, Washington, D.C., 1997. FEMA 302., "NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures," Federal Emergency Management Agency, Washington, D.C., 1997. FEMA-355C., "State of the Art Report on Systems Performance of Steel Moment Frames Subject to Earthquake Ground Shaking," September, 2000. FEMA-355E., "State of the Art Report on Past Performance of Steel Moment-Frame Buildings in Earthquakes," September 2000. FEMA-355F., "State of the Art Report on Performance Prediction and Evaluation of Steel Moment-Frame Buildings," September 2000. Humar, J.L. and Wright, E.W., "Earthquake Response of Steel Framed Multistory Building with Setbacks," Earthquake Engineering and Structural Dynamic, Vol.5, pp. 15-39, 1977. Magliulo,G., Ramasco, R. and Realfonzo, R., "Seismic Behavior of Irregular in Elevation Plane Frames," Proceedings, 12th European Conference On Earthquake Engineering, Paper No. 219, European Association for Earthquake Engineering , London, Elsevier, Oxford, U.K. , 2002. Miranda E., M.S. and Reyes, C. J. , "Approximate Lateral Drift In Multistory Building with Uniform Stiffness," Journal of Structural Engineering, ASCE, Vol. 128, July 2002, pp. 840-849,. Moehle, J. P., "Seismic Response of Vertically Irregular Structures," Journal of Structural Engineering, ASCE, Vol. 110, September 1984. Moehle, J. P. and Alarcon, L. F., "Seismic analysis methods for irregular buildings" Journal of Structural Engineering, ASCE, Vol. 112(1) 1986, pp. 35-52. Naeim, F., "The Seismic Design Handbook, 2nd Edition", Chapman Hall, 1989. Osman, A. M., "Seismic Response of Steel Frames with Symmetric Setback," Proceedings, 7th US National Conference on Earthquake Engineering, Paper No. 367, Boston, Earthquake Engineering Research Institute (EERI), Oakland, California, 2002. Pito, D. & Costa, A.G., "Influence of Vertical Irregularities on Seismic Response of Buildings," Proceedings, Tenth European Conference on Earthquake Engineering, A.A. Balkema, Rotterdam, Vol. 2.1995. Tremblay, R. & Poncet, L., "Seismic Performance of Concentrically Braced Steel Frames in Multistory Buildings with Mass Irregularity," Journal of Structural Engineering, ASCE, Vol. 131, No. 9, September, 2005. SAP 2000., "Integrated Finite Element Analysis and Design Structures Analysis Reference," Computer and Structures , Berkeley, California , 1998. Shahrooz, B.M. and Moehle, J.P. , "Seismic Response and Design of Setback Buildings," Journal of Structural Engineering, ASCE,Vol.6, No.5, May,1990. International Council of Building Officials, "Uniform Building Code (UBC)," Whittier, California, April, 1997. Valmundsson, E.V. and Nau, J.M., "Seismic Response of Building Frames with Vertical Structural Irregularities.," Journal of Structural Engineering, ASCE, 123(1):30-41, 1997. Wong, C.M. and Tso, W.K., "Seismic Loading For Buildings with Setback," Canadian Journal of Civil Engineering, Vol. 21, No. 5, October,1994. Wood, S.L., "Dynamic Response of R/C Frames with Irregular Profiles," Proceedings, Third U.S. National Conference on Earthquake Engineering, August, 1986. Youssef, N.F.G., Bonowitz, D. and Gross, J.L., "A Survey of Steel Moment Resisting Frames Buildings," National Institute of Standards and Technology, Gaithersburg, 1995. Read More